Finite Group Databasebeta

← C2×C11×#1697 #14596331

Subgroups — C2×C11×#1697 #14596331

Order 2816.

778 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#486C211yesmaximal, characteristic, complemented
2C2×C11×#476C211yesmaximal, characteristic, complemented
3C2×C11×#459C211yesmaximal, characteristic
4C2×C11×#436C211yesmaximal, characteristic, complemented
5C11×#1697C218yesmaximal, direct product factor
6C2×C11×#335C211yesmaximal, characteristic, complemented
7C2×C11×#333C211yesmaximal, characteristic, complemented
8C2×C11×#331C211yesmaximal, characteristic, complemented
9C22×C11×D8—21no—
10C22×C11×M16—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×#127C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C11×#486—22no—
15C11×#486C2214yescomplemented
16C11×#476—22no—
17C11×#476C2214yescomplemented
18C11×#459—22no—
19C11×#459C2214yes—
20C11×#436—22no—
21C11×#436C2214yescomplemented
22C2×C11×#106—21no—
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#102—21no—
27C2×C11×#102—21no—
28C2×C11×#102—21no—
29C2×C11×#102—21no—
30C2×C11×C22⋊C8—21no—
31C2×C4×C8×C11C2211yescharacteristic
32C11×#335C2214yescomplemented
33C11×#333C2214yescomplemented
34C11×#331C2214yescomplemented
35C22×Q8×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11D411yescharacteristic
40C23×C4×C11—21no—
41C2×C11×D8—24no—
42C2×C11×D8—44no—
43C2×C11×M16—24no—
44C2×C11×M16—44no—
45C22×C8×C11—21no—
46C22×C8×C11—21no—
47C22×C8×C11—21no—
48C22×C8×C11D411yescharacteristic
49C22×C8×C11D411yescharacteristic
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8C2312yes—
54C11×#127—21no—
55C11×#127—21no—
56C11×#127—21no—
57C11×#127C2312yes—
58C4×D4×C11—21no—
59C4×D4×C11—21no—
60C4×D4×C11D412yes—
61C4×D4×C11C2312yes—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C42×C11C2311yescharacteristic
67C11×#106—24no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8—21no—
71C11×C4⋊C8C2312yes—
72C11×C4⋊C8C2312yes—
73C11×C4⋊C8C2312yes—
74C11×#102—24no—
75C11×#102—24no—
76C11×#102—24no—
77C11×#102—24no—
78C11×C22⋊C8—24no—
79C4×C8×C11D412yes—
80C4×C8×C11C2312yes—
81C2×#1697C1111yesmaximal, characteristic, direct product factor, Sylow
82C24×C11—21no—
83C24×C11—41no—
84C2×Q8×C11—22no—
85C2×Q8×C11—41no—
86C2×Q8×C11—82no—
87C2×D4×C11—21no—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—22no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—42no—
97C2×D4×C11—42no—
98C2×D4×C11—42no—
99C2×D4×C11—42no—
100C2×D4×C11—82no—
101C2×D4×C11C2×D412yes—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11—41no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C11×D8—48no—
112C11×M16—48no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—42no—
119C2×C8×C11—42no—
120C2×C8×C11—42no—
121C2×C8×C11C2×D412yes—
122C2×C8×C11C2×D412yes—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4C2×D412yes—
129C11×C22⋊C4—22no—
130C11×C22⋊C4—22no—
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133C42×C11#4111yescharacteristic
134C42×C11C2411yescharacteristic
135C2×#486C2×C1111yescharacteristic, complemented
136C2×#476C2×C1111yescharacteristic, complemented
137C2×#459C2×C1111yescharacteristic
138C2×#436C2×C1111yescharacteristic, complemented
139#1697C2×C1118yesdirect product factor
140C2×#335C2×C1111yescharacteristic, complemented
141C2×#333C2×C1111yescharacteristic, complemented
142C2×#331C2×C1111yescharacteristic, complemented
143C23×C11—22no—
144C23×C11—42no—
145C23×C11—42no—
146C23×C11—42no—
147C23×C11—42no—
148C23×C11—82no—
149C23×C11—82no—
150C23×C11—82no—
151C23×C11#12111yescharacteristic
152Q8×C11—82no—
153Q8×C11—82no—
154D4×C11—22no—
155D4×C11—22no—
156D4×C11—42no—
157D4×C11—42no—
158D4×C11—42no—
159D4×C11—42no—
160D4×C11—42no—
161D4×C11—82no—
162D4×C11—82no—
163D4×C11—82no—
164D4×C11—82no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—44no—
171C2×C4×C11—42no—
172C2×C4×C11—82no—
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#13512yes—
177C2×C4×C11AGL(1,ℤ/8)12yes—
178C2×C4×C11AGL(1,ℤ/8)12yes—
179C2×C4×C11#13712yes—
180C2×C4×C11C22×D411yescharacteristic
181C2×C4×C11C22×D411yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C8×C11—22no—
184C8×C11—22no—
185C8×C11—42no—
186C8×C11—42no—
187C8×C11—42no—
188C22×D8—21no—
189C22×M16—21no—
190C2×C4⋊Q8C22×C1111yescharacteristic
191C2×#127C22×C1111yescharacteristic
192C2×C4×D4C22×C1111yescharacteristic
193#486—22no—
194#486C22×C1114yescomplemented
195#476—22no—
196#476C22×C1114yescomplemented
197#459—22no—
198#459C22×C1114yes—
199#436—22no—
200#436C22×C1114yescomplemented
201C2×#106—21no—
202C2×C4⋊C8C22×C1111yescharacteristic
203C2×C4⋊C8C22×C1111yescharacteristic
204C2×C4⋊C8C22×C1111yescharacteristic
205C2×#102—21no—
206C2×#102—21no—
207C2×#102—21no—
208C2×#102—21no—
209C2×C22⋊C8—21no—
210C2×C4×C8C22×C1111yescharacteristic
211#335C22×C1114yescomplemented
212#333C22×C1114yescomplemented
213#331C22×C1114yescomplemented
214C22×C11—42no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—84no—
218C22×C11—82no—
219C22×C11—82no—
220C22×C11—82no—
221C22×C11—164no—
222C22×C11#46312yes—
223C22×C11#46812yes—
224C22×C11#47212yes—
225C22×C11C2×#12111yescharacteristic
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—42no—
229C4×C11—82no—
230C4×C11#46312yes—
231C4×C11#46812yes—
232C4×C11C2×#13511yescharacteristic
233C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
234C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
235C4×C11C2×#13711yescharacteristic
236C22×Q8—21no—
237C22×D4—21no—
238C22×D4—21no—
239C22×D4—21no—
240C22×D4D4×C1111yescharacteristic
241C23×C4—21no—
242C2×D8—24no—
243C2×D8—44no—
244C2×M16—24no—
245C2×M16—44no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8D4×C1111yescharacteristic
250C22×C8D4×C1111yescharacteristic
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8C23×C1112yes—
255#127—21no—
256#127—21no—
257#127—21no—
258#127C23×C1112yes—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4D4×C1112yes—
262C4×D4C23×C1112yes—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4D4×C1111yescharacteristic
266C2×C22⋊C4—21no—
267C2×C42C23×C1111yescharacteristic
268#106—24no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8C23×C1112yes—
273C4⋊C8C23×C1112yes—
274C4⋊C8C23×C1112yes—
275#102—24no—
276#102—24no—
277#102—24no—
278#102—24no—
279C22⋊C8—24no—
280C4×C8D4×C1112yes—
281C4×C8C23×C1112yes—
282C2×C11—82no—
283C2×C11—162no—
284C2×C11#169714yesdirect product factor
285C2×C11C2×#46311yescharacteristic
286C2×C11C2×#46811yescharacteristic
287C2×C11C2×#47211yescharacteristic
288C24—21no—
289C24—41no—
290C2×Q8—22no—
291C2×Q8—41no—
292C2×Q8—82no—
293C2×D4—21no—
294C2×D4—22no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—42no—
303C2×D4—42no—
304C2×D4—42no—
305C2×D4—42no—
306C2×D4—82no—
307C2×D4C2×D4×C1112yes—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—41no—
314C22×C4C2×D4×C1111yescharacteristic
315C22×C4C2×D4×C1111yescharacteristic
316C22×C4C11×#4111yescharacteristic
317D8—48no—
318M16—48no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—42no—
325C2×C8—42no—
326C2×C8—42no—
327C2×C8C2×D4×C1112yes—
328C2×C8C2×D4×C1112yes—
329C4⋊C4—21no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4C2×D4×C1112yes—
335C22⋊C4—22no—
336C22⋊C4—22no—
337C42C2×D4×C1111yescharacteristic
338C42C2×D4×C1111yescharacteristic
339C42C11×#4111yescharacteristic
340C42C24×C1111yescharacteristic
341C11C2×#169711yescharacteristic, direct product factor, Sylow
342C23—22no—
343C23—42no—
344C23—42no—
345C23—42no—
346C23—42no—
347C23—82no—
348C23—82no—
349C23—82no—
350C23C11×#12111yescharacteristic
351Q8—82no—
352Q8—82no—
353D4—22no—
354D4—22no—
355D4—42no—
356D4—42no—
357D4—42no—
358D4—42no—
359D4—42no—
360D4—82no—
361D4—82no—
362D4—82no—
363D4—82no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—44no—
370C2×C4—42no—
371C2×C4—82no—
372C2×C4C11×#12111yescharacteristic
373C2×C4C11×#12111yescharacteristic
374C2×C4C11×#12111yescharacteristic
375C2×C4C11×#13512yes—
376C2×C4C11×AGL(1,ℤ/8)12yes—
377C2×C4C11×AGL(1,ℤ/8)12yes—
378C2×C4C11×#13712yes—
379C2×C4C22×D4×C1111yescharacteristic
380C2×C4C22×D4×C1111yescharacteristic
381C2×C4C2×C11×#4111yescharacteristic
382C8—22no—
383C8—22no—
384C8—42no—
385C8—42no—
386C8—42no—
387C22—42no—
388C22—42no—
389C22—42no—
390C22—84no—
391C22—82no—
392C22—82no—
393C22—82no—
394C22—164no—
395C22C11×#46312yes—
396C22C11×#46812yes—
397C22C11×#47212yes—
398C22C2×C11×#12111yescharacteristic
399C4—21no—
400C4—21no—
401C4—42no—
402C4—82no—
403C4C11×#46312yes—
404C4C11×#46812yes—
405C4C2×C11×#13511yescharacteristic
406C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
407C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
408C4C2×C11×#13711yescharacteristic
409C2—82no—
410C2—162no—
411C2C11×#169714yesdirect product factor
412C2C2×C11×#46311yescharacteristic
413C2C2×C11×#46811yescharacteristic
414C2C2×C11×#47211yescharacteristic
subgroupG/H
center, socleC23×C11#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC2×C11×#459C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C11×#486C2semidirect
2. C2×C11×#476C2semidirect
4. C2×C11×#436C2semidirect
5. C11×#1697C2direct (N × H)
6. C2×C11×#335C2semidirect
7. C2×C11×#333C2semidirect
8. C2×C11×#331C2semidirect
15. C11×#486C22semidirect
17. C11×#476C22semidirect
21. C11×#436C22semidirect
32. C11×#335C22semidirect
33. C11×#333C22semidirect
34. C11×#331C22semidirect
81. C2×#1697C11direct (N × H)
135. C2×#486C2×C11semidirect
136. C2×#476C2×C11semidirect
138. C2×#436C2×C11semidirect
139. #1697C2×C11direct (N × H)
140. C2×#335C2×C11semidirect
141. C2×#333C2×C11semidirect
142. C2×#331C2×C11semidirect
194. #486C22×C11semidirect
196. #476C22×C11semidirect
200. #436C22×C11semidirect
211. #335C22×C11semidirect
212. #333C22×C11semidirect
213. #331C22×C11semidirect
284. C2×C11#1697direct (N × H)
341. C11C2×#1697direct (N × H)
411. C2C11×#1697direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C11×#4862
C2×C11×#4762
C2×C11×#4592
C2×C11×#4362
C11×#16972
C2×C11×#3352
C2×C11×#3332
C2×C11×#3312
C2×#169711